Abstract

Spinning is one of the most effective and well-known ways to reduce polarization mode dispersion of optical fibers. In spite of the popularity of spinning, a detailed theory of spin effects is still lacking. We report an analytical expression for the mean differential group delay of a randomly birefringent spun fiber. The result holds for any periodic spin function with a period shorter than the fiber’s beat length.

© 2002 Optical Society of America

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References

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  1. A. Galtarossa, L. Palmieri, and A. Pizzinat, J. Lightwave Technol. 19, 1502 (2001).
    [CrossRef]
  2. A. Galtarossa, L. Palmieri, A. Pizzinat, M. Schiano, and T. Tambosso, J. Lightwave Technol. 18, 1389 (2000).
    [CrossRef]
  3. M. J. Li and D. A. Nolan, Opt. Lett. 23, 1659 (1998).
    [CrossRef]
  4. P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
    [CrossRef]
  5. A. Galtarossa and L. Palmieri have prepared a paper entitled “Measure of twist-induced circular birefringence in long single-mode fibers: theory and experiments,” for submission to J. Lightwave Technol.
  6. B. Øksendal, Stochastic Differential Equations (Springer-Verlag, Berlin, 2000).
  7. V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, New York, 1975).
  8. A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, Opt. Lett. 25, 1322 (2000).
    [CrossRef]
  9. F. Corsi, A. Galtarossa, and L. Palmieri, J. Opt. Soc. Am. A 16, 574 (1999).
    [CrossRef]
  10. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).
  11. C. R. Menyuk, Technology Research Center, University of Maryland, Baltimore County, Baltimore, Md. 21227 (personal comminucation).

2001 (1)

2000 (2)

1999 (1)

1998 (1)

1996 (1)

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Corsi, F.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

Galtarossa, A.

Li, M. J.

Menyuk, C. R.

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

C. R. Menyuk, Technology Research Center, University of Maryland, Baltimore County, Baltimore, Md. 21227 (personal comminucation).

Nolan, D. A.

Øksendal, B.

B. Øksendal, Stochastic Differential Equations (Springer-Verlag, Berlin, 2000).

Palmieri, L.

Pizzinat, A.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

Schiano, M.

Starzhinskii, V. M.

V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, New York, 1975).

Tambosso, T.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

Wai, P. K. A.

P. K. A. Wai and C. R. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Yakubovich, V. A.

V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, New York, 1975).

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (1)

Opt. Lett. (2)

Other (5)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

C. R. Menyuk, Technology Research Center, University of Maryland, Baltimore County, Baltimore, Md. 21227 (personal comminucation).

A. Galtarossa and L. Palmieri have prepared a paper entitled “Measure of twist-induced circular birefringence in long single-mode fibers: theory and experiments,” for submission to J. Lightwave Technol.

B. Øksendal, Stochastic Differential Equations (Springer-Verlag, Berlin, 2000).

V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients (Wiley, New York, 1975).

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Figures (2)

Fig. 1
Fig. 1

Evolution of the mean DGD as a function of distance for a spun fiber, with LF=3 m and spin function Az=A0 sin2πz/p, where A0=4.8 rad and p=4 m. The beat length was set such that Δτun=54 fs for a length of 5 km. The continuous curve refers to Eq. (1); triangles and circles are numerical estimates of the mean DGD obtained from the first and the second models of birefringence, respectively.

Fig. 2
Fig. 2

Evolution of Φ as a function of spin amplitude for the spin function given in Eq. (6) with p=4 m. Continuous curves from top to bottom, refer to LF=0.1, 0.3, 0.8, and 2 m. Dashed curve, LF+.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Δτ=C2+S2C1/2Δτun,
C=γp20p0pexp-2σ2ucosAt-At-udtdu,S=γp20p0pexp-2σ2usinAt-At-udtdu,
dΩ¯dz=-2σ2αz0-αz-2σ2-b0b0Ω¯+bω00,
dy¯dz=-2σ2αz-αz-2σ2y¯z+bω1C-1S,
y¯z=bωI-Rz,0-10pRz,p-tf¯dt,
Yz=exp-2σ2zcos Azsin Az-sin Azcos Az.
Φ=C2+S2C1/2,
Az=A0sin2πzp+cos4πzp
S1p20p0psinAt-At-udtdu=0,
C1p0pcos Audu2+1p0psin Audu2.

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